Three circular tables are placed against a wall, such that each table exactly touches the wall and the other two tables. The distance between the points where the two larger tables touch the wall is precisely 300cm. Given that the radius of each table is a whole number, how big are the tables?

# Puzzle of the Week #112 - Number Fill-In

Place the twelve 6-digit numbers into the grid (one digit in each cell), half of them left-to-right and half of them top-to-bottom.

What is the 6-digit number to be found along the main diagonal (from top-left to bottom-right)?

# Puzzle of the Week #111 - Third Avenue

Draw a path that visits every dot once only. The path will be made only of horizontal and vertical lines. The path cannot cross itself or branch off, and must return to the start to form a complete circuit. Every **third** turning point in the circuit path has been marked by a triangle symbol.

# Puzzle of the Week #110 - Finding the Ellipse

It is well-known that a circle can be uniquely defined by three points on its circumference, providing they are not collinear.

I have ascertained that the analogous number of points needed to uniquely define an ellipse is five, with the condition that each of those five points lies strictly outside the quadrilateral formed by the other four.

What I don’t know is how, given the planar coordinates of the five points, you could discover other information about the ellipse, such as axis lengths, orientation and position. I’m not at all sure there is a method that will work in the general case.

In some specific cases, it is possible to work out the position, orientation and axes of the ellipse, given the co-ordinates of five points.

For instance, given the points (1,0), (2,0), (0,1), (0,2) and (1,2) lying on an ellipse, find the length of the minor axis.

# Puzzle of the Week #109 - Fetching and Carrying

Three people have to carry five boxes a distance of 120m from point A to point B. They each travel at a speed of 1m/s when carrying a box, or 2m/s when returning empty-handed for another box. Each person can carry only one box at a time.

What is the minimum time it will take them to carry all five boxes to point B?

*People often ask where I get the ideas for my puzzles. This one has a typically mundane origin: I was bringing grocery shopping in from the car with my two children. There was more than we could manage in one trip so return trips were necessary. I started to wonder whether dropping groceries partway to the kitchen might be more efficient. We didn’t implement such a solution, but it did get me thinking about how I could reformulate the question as a puzzle, so here we are.*

# Puzzle of the Week #108 - Enigma Wordsearch

Just one instance of one word to find: ENIGMA

# Puzzle of the Week #107 - Pipework Problems

This is a real life problem I encountered in my job. To try to make explain it I’ll talk in terms of x,y,z coordinates.

There is one pipe heading from the negative–x direction towards the (0,0,0) origin point. 100mm before it reaches the origin, the pipe bends such that the radius of the centre line of the pipe is 100mm. After 90 degrees it straightens out so that it is heading on the +y axis.

A second pipe is heading from the +x direction towards the origin. Again it bends with a centre line radius of 100mm for 90 degrees before heading on the +z axis.

What is the minimum distance between the pipes' centre lines? I’ll be happy with 1 decimal place.

# Puzzle of the Week #106 - Class Size Paradox

Some students (fewer than 100 in total) were split into two classes.

The simple mean average between the sizes of the two classes was noted.

Each of the students was asked how large their class was, and the mean average of their responses was calculated, and was found to be precisely 7 more than the simple mean average.

How many students were in each of the two classes?

# Puzzle of the Week #105 - Eight Daughters

A wealthy old woman died, and in her will she divided her fortune amongst her eight daughters. The total amount to be divided was less than 10000 ducats, and each daughter received a whole number of ducats according to the following:

The eldest daughter received 1/15 of the total.

The second daughter received 1/13 of what remained after the first daughter’s share was removed.

The third daughter received 1/11 of what remained after the previous daughters’ shares were taken.

The fourth daughter received 1/9 of what then remained.

The fifth daughter received 1/7 of what then remained.

The sixth daughter received 1/5 of what then remained.

The seventh daughter received 1/3 of what then remained.

Finally the youngest, favourite daughter received all of the remaining fortune.

How much did the youngest daughter receive?

# Puzzle of the Week #104 - Paddocks

Draw fences between some of the posts so that each post is at the junction of exactly **THREE** fences.

These fences will divide the field into several **PADDOCKS**; any paddock whose area is greater than a single triangle will contain a **NUMBER**, which will indicate the area of the paddock, or in other words the number of **TRIANGLES** that make up the paddock.

The boundary fence is already in place, so any post on the boundary only needs one more fence emerging from it in order to make up its full complement.

Please visit and like my facebook page: https://www.facebook.com/elliottlinepuzzles/

# Puzzle of the Week #103 - Minimal Triangle

I have a triangle which contains two circles of radius 1, which do not overlap each other or the edges of the triangle.

The triangle has the least possible PERIMETER to contain those circles.

What is the perimeter?

# Puzzle of the Week #102 - Shadowbox

Chances are you've never met a Shadowbox puzzle before, as it is my own invention, so I'll explain how they work.

Despite looking like crosswords, they are logic puzzles rather than word puzzles, since you don't need to be familiar with any of the words, or know their meanings.

The idea behind the puzzles is actually very simple: you need to fit all of the listed words into the grid, in a crossword style (ie. all words reading left-right or downwards, forming a lattice, with black squares in between). However, you must construct the grid of black squares and letter squares as you go along, using just three very simple rules:

1: A grey squares means that the square will either become a black square, or else it will contain a vowel (A, E, I, O, U).

2: A white square will definitely contain a consonant.

3: The final pattern of black squares and letter squares will be symmetrical in horizontal, vertical and diagonal directions.

Please visit and like https://www.facebook.com/elliottlinepuzzles/ Send me a message on that page if you think you have the answer, and I'll let you know if you're correct.

If you enjoyed this puzzle, I have good news for you: I published an entire book of 100 of them, which you can find here: http://www.lulu.com/shop/elliott-line/shadowbox-logical-crossword-puzzles/paperback/product-20347753.html or here https://www.amazon.co.uk/Shadowbox-Logical-Crossword-Puzzles-Elliott/dp/1447861965/

# Puzzle of the Week #101 - Paddocks

Another bonus 'Puzzle of the Week'.

Draw fences between some of the posts so that each post is at the junction of exactly **THREE** fences.

These fences will divide the field into several **PADDOCKS**; any paddock whose area is greater than a single triangle will contain a **NUMBER**, which will indicate the area of the paddock, or in other words the number of **TRIANGLES** that make up the paddock.

The boundary fence is already in place, so any post on the boundary only needs one more fence emerging from it in order to make up its full complement.

Please visit and like https://www.facebook.com/elliottlinepuzzles/ Send me a message on that page if you think you have the answer, and I'll let you know if you're correct.

# Puzzle of the Week #100 - Quotebreaker

I have taken a short passage of text and encoded it according to the table below. Your task is to decode it. Be careful, as some sequences of numbers could lead to several words, for instance 31110 could mean CAT (3,1,110), but could equally mean MAD (31,1,10).

## 1102013223 12133111 1233102 1122110321110213213 31121 1032111011. 21 203310011 12133111 20111211 113222331211110 31121 1001111221223011103 1103 31111320 1103 21 113222331211110 31123213213 110201131. 201110211'103 11033 1102011 3211120110 333211 2011132101021110!

Please visit and like https://www.facebook.com/elliottlinepuzzles/ Send me a message on that page if you think you have the answer, and I'll let you know if you're correct.

# Solutions

You may have noticed that I don't very often post solutions to my Puzzle of the Week puzzles, for which I can only apologise.

If you would like a solution to a particular puzzle, leave comment letting me know and I'll do my best to help.

I try to encode my solutions using https://www.base64encode.org/ so that people don't stumble across the solution accidentally. You are very welcome to post solutions yourself in the comments, but if possible please encode it (obviously only really possible with text-based solutions).

Many thanks

Elliott

# Puzzle of the Week #99 - Paddocks

Another bonus 'Puzzle of the Week'.

Draw fences between some of the posts so that each post is at the junction of exactly **THREE** fences.

These fences will divide the field into several **PADDOCKS**; any paddock whose area is greater than a single triangle will contain a **NUMBER**, which will indicate the area of the paddock, or in other words the number of **TRIANGLES** that make up the paddock.

The boundary fence is already in place, so any post on the boundary only needs one more fence emerging from it in order to make up its full complement.

Why not visit https://www.facebook.com/elliottlinepuzzles/

# Calling Paddocks Fans

A question for you: I'm busy putting together a new book of puzzles (and then trying to get it published or self-published).

Should it be a wide assortment of puzzles like my Puzzle of the Week?

Should it be a mixture of Paddocks and other original map/maze/grid/path style logic puzzles?

Or should it be primarily or even exclusively Paddocks puzzles?

All comments welcome!

# Puzzle of the Week #98 - Strange Digits

You might need a calculator for this one

[1]+[2]+[3] = 12

[2]+[3]+[4] = 14

[3]+[4]+[5] = 14

[4]+[5]+[1] = 11

[5]+[1]+[2] = 12

What is [8]?

Why not visit https://www.facebook.com/elliottlinepuzzles/ where you'll be able to send me your solution, and I'll let you know if you're correct.

Update: solution now in comments

# Puzzle of the Week #97 - Paddocks

I usually publish a puzzle each Friday, but here's a bonus one:

Draw fences between some of the posts so that each post is at the junction of exactly **THREE** fences.

These fences will divide the field into several **PADDOCKS**; any paddock whose area is greater than a single triangle will contain a **NUMBER**, which will indicate the number of **TRIANGLES** that make up the paddock.

Why not visit https://www.facebook.com/elliottlinepuzzles/

# Alex Bellos' 'Can You Solve It?' Guardian Column

I'm delighted that the maths/puzzle writer Alex Bellos has used some of my puzzles in his Guardian column.

https://www.theguardian.com/science/2017/may/08/can-you-solve-it-have-a-punt-on-the-paddocks-puzzle

Thanks Alex!